Question: $ D = \left[\begin{array}{rr}-2 & 0 \\ 0 & 2 \\ 0 & 1\end{array}\right]$ $ A = \left[\begin{array}{rr}-1 & 4 \\ -1 & 1\end{array}\right]$ Is $ D A$ defined?
In order for multiplication of two matrices to be defined, the two inner dimensions must be equal. If the two matrices have dimensions $( m \times  n)$ and $( p \times q)$ , then $ n$ (number of columns in the first matrix) must equal $ p$ (number of rows in the second matrix) for their product to be defined. How many columns does the first matrix, $ D$ , have? How many rows does the second matrix, $ A$ , have? Since $ D$ has the same number of columns (2) as $ A$ has rows (2), $ D A$ is defined.